Frequency analysis of a motorbike under motion conditions

Frequency analysis is of uttermost importance when dealing with controllability of a dynamic system in changing working domains. This becomes relevant due to the non-linearity in damping, stiffness and inertia properties of mechanisms with broad motion and under heavy external conditions, such as a motorbike running on off-road terrains, braking and transmitting traction to uneven road profiles. A relatively simple but complete planar model of the vehicle on uneven terrain has been here adopted, which takes into account the whole dynamics and non-linear rigid body kinematics of the motorbike. This complete planar model is the computational engine for running the eigenvalue analysis of the time-varying eigenproblem. Tracking the eigensolution variability along the working space becomes a relevant insight on the behaviour of the motorbike under the different conditions. Theoretical formulation and simulations are discussed in detail.